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A recently developed method has been extended to a nonlocal equation arisingin steady water wave propagation in two dimensions. We obtain analyicapproximation of steady water wave solution in two dimensions with rigorouserror bounds for a set of parameter values that correspond to heights slightlysmaller than the critical. The wave shapes are shown to be analytic. The methodpresented in quite general and does not assume smallness of wave height orsteepness and can be readily extended to other interfacial problems involvingLaplace's equation.

Analytical Approximation for 2-D Nonlinear Periodic Deep Water Waves